In this paper, positive singular systems in both continuous and discrete cases are addressed, and a complete characterization for stability is provided. First, it is shown that positive singular systems can be stable for a non-negative initial condition. The presented stability criteria are necessary and sufficient, and can be checked by means of linear matrix inequality (LMI) or linear programming (LP). Further, we generalize the Lyapunov stability theory for positive singular systems.

中文翻译：

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正奇异系统稳定性的Drazin逆条件

本文讨论了连续和离散情况下的正奇异系统，并提供了稳定性的完整表征。首先，证明了正奇异系统对于非负初始条件可以是稳定的。提出的稳定性标准是必要和充分的，可以通过线性矩阵不等式（LMI）或线性规划（LP）进行检查。此外，我们推广了正奇异系统的Lyapunov稳定性理论。